which source is normally the brighter. In this process of comparison the term ci\ 5 of equation (1) is embodied as one of the calibration constants of the instrument. Radiation Pyrometer Temperature Scale.— The temperature scale for the radiation pyrometer is based upon the Stefan-Boltzmann law expressing the relation between the total energy J radiated per unit time per unit area by a black body and its absolute temperature, #° absolute, as follows:
J = cr(tf4 - <V) (4)
Where $0 denotes the absolute temperature of the surroundings or of the measuring instrument receiving the radiation, and cr an empirical constant. In general <V is negligible in comparison with #4 so the above relation becomes:
For a non-black body we have:
J' = o-E&* = aS4 • (6)
where E is the total emissivity and S is the apparent absolute temperature of the object sighted upon as measured by the radiation pyrometer. From (6) one obtains :
E = £4/#4 or log E = 4 (log S - log #) (7)
Thus knowing the total emissivity E of any material it is possible to obtain the true temperature # from the apparent temperature S as measured by a radiation pyrometer.
Summary Statement of the Two Radiation Laws. — Equation (1) states that the intensity of radiation of a fixed wave length from a black body is proportional to
Equation (5) states that the "total radiation of all wave lengths emitted by a black body is proportional to $4. These two laws which form the basis of optical and radiation pyrometry respectively are in agreement with the temperature scale defined by the gas thermometer up to 1,550°C., the upper limit at which a gas thermometer has been used satisfactorily. Above this range to 2,500°C. the scales defined by these two laws have been found, experimentally, to be in mutual agreement, and it is believed that they correctly represent the thermodynamic scale for all temperatures.
Fery Optical Pyrometer. — Figure 16 illustrates the principle of the Fery optical pyrometer. G is a means for producing a divided photometric field. In the later instruments a Lummer-Brodhun or silver strip cube is employed. Part of the field of view is illuminated by the source sighted upon and part by the gasoline lamp L which burns at a constant brightness. By moving the wedges of black glass, pp'} the thickness of absorbing glass in the line of sight can be varied until the part of the field illuminated by the source has the same brightness as that illuminated by the lamp. A red-glass screen is used in the ocular so that fairly monochromatic light of this color (0.65/* to 0.63/i) is compared. The relation between the thickness of the wedges x read on a scale and the absolute
temperature $ is x + P = — where P and Q are constants determinable by two
calibration points. The instrument must be focused upon the radiating source but no corrections for sighting distance need be applied. The Le Chatelier optical pyrometer is similar in principle but is not of constant aperture and important corrections must be made with change of focus.